Material fabrication using acoustic radiation forces

ABSTRACT

Apparatus and methods for using acoustic radiation forces to order particles suspended in a host liquid are described. The particles may range in size from nanometers to millimeters, and may have any shape. The suspension is placed in an acoustic resonator cavity, and acoustical energy is supplied thereto using acoustic transducers. The resulting pattern may be fixed by using a solidifiable host liquid, forming thereby a solid material. Patterns may be quickly generated; typical times ranging from a few seconds to a few minutes. In a one-dimensional arrangement, parallel layers of particles are formed. With two and three dimensional transducer arrangements, more complex particle configurations are possible since different standing-wave patterns may be generated in the resonator. Fabrication of periodic structures, such as metamaterials, having periods tunable by varying the frequency of the acoustic waves, on surfaces or in bulk volume using acoustic radiation forces, provides great flexibility in the creation of new materials. Periodicities may range from millimeters to sub-micron distances, covering a large portion of the range for optical and acoustical metamaterials.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a divisional of U.S. patent application Ser. No.13/047,684 entitled “Material Fabrication Using Acoustic RadiationForces” filed Mar. 14, 2011, which claims the benefit of and priority toU.S. Provisional Patent Application No. 61/340,113 for “AcousticallyEngineered Materials Using Acoustic Radiation Force” which was filed onMar. 12, 2010. The entire contents of the above listed applications arehereby specifically incorporated by reference herein for all that theydisclose and teach.

STATEMENT REGARDING FEDERAL RIGHTS

This invention was made with government support under Contract No.DE-AC52-06NA25396 awarded by the U.S. Department of Energy. Thegovernment has certain rights in the invention.

BACKGROUND OF THE INVENTION

Metamaterials are periodic materials having artificially fabricatedinclusions in a host medium or on a host surface, that derive theirproperties, such as mechanical, optical and electrical properties, fromthe spatial distribution of the inclusions as well as from theproperties of the subunits, as opposed to the properties of thecomponents alone. Examples of man-made materials that do not exist innature include sonic or phononic crystals (periodicity on the millimeterscale) and photonic crystals (periodicity on the sub-micrometer scale).Sonic crystals have a finite-sized periodic array of sonic scatterersembedded in a homogeneous host material and may have spectral gaps,which can be tuned by varying the size and geometry of the material,which prevent the transmission of sound waves having certainfrequencies. If the host material is a solid, the term ‘phononiccrystal’ is used for the artificial crystals, and both longitudinal andtransverse shear waves may exist and may be coupled with one another. Bycontrast, for sonic crystals such waves are considered to beindependent, and the scatterers are typically solid materials disposedin a fluid. A sonic crystal may be considered to be a sonic version of aphotonic crystal, photonic crystals being periodic opticalnanostructures having regularly repeating internal regions of high andlow dielectric constant which affect the motion of photons in a similarway that periodicity of a semiconductor crystal affects the motion ofelectrons. Photons may be transmitted through such structures dependingon their wavelength. Photonic and phononic effects occur when thespacing of the periodic structures is of the order of the wavelength ofthe photons or sound waves, respectively.

Photolithography and etching techniques similar to those used forintegrated circuits have been used for fabricating three-dimensionalphotonic crystals. Photonic crystals have also been generated asself-assembled structures from colloidal crystals.

SUMMARY OF THE INVENTION

Embodiments of the present invention overcome the disadvantages andlimitations of the prior art by providing apparatuses and methods forcreating periodic structures having periodicities from millimeters tosub-micron lengths on surfaces and in three-dimensions.

It is further an object of embodiments of the present invention toprovide an apparatus and method for creating such periodic structures insuch a manner that acoustical and optical materials can be fabricated.

Additional objects, advantages and novel features of the invention willbe set forth in part in the description which follows, and in part willbecome apparent to those skilled in the art upon examination of thefollowing or may be learned by practice of the invention. The objectsand advantages of the invention may be realized and attained by means ofthe instrumentalities and combinations particularly pointed out in theappended claims.

To achieve the foregoing and other objects, and in accordance with thepurposes of the present invention, as embodied and broadly describedherein, the method for fabricating materials, hereof, includes:suspending particles in a solidifiable fluid; generating at least oneacoustic standing wave having a chosen wavelength in the fluid for asufficient time that the suspended particles migrate to at least onepressure node of the standing wave or to at least one pressure antinodeof the standing wave; and solidifying the fluid.

In another aspect of the present invention and in accordance with itsobjects and purposes, the apparatus for fabricating materials, hereof,includes: an acoustic resonator cavity for containing a static quantityof a suspension of particles in a solidifiable fluid; means forgenerating at least one acoustic standing wave having a chosenwavelength in the liquid for a sufficient time that the suspendedparticles migrate to at least one pressure node or at least one pressureantinode of the at least one standing wave forming a pattern; whereinthe fluid is solidified to fix the pattern.

Benefits and advantages of embodiments of the present invention include,but are not limited to, providing apparatus and methods for usingacoustic radiation forces to order particles suspended in a host fluid,wherein the particles may range in size from nanometers to millimeters,and may have any shape. The resulting pattern may be may be rapidlygenerated, typical times ranging from a few seconds to a few minutes,and fixed by using a solidifiable host fluid. Many complex particlearrangements are possible, including acoustic and optical metamaterialshaving periodic structures ranging from millimeters to sub-microndistances, from an inexpensive, bench-top system.

BRIEF DESCRIPTION OF THE DRAWINGS

The accompanying drawings, which are incorporated in and form a part ofthe specification, illustrate the embodiments of the present inventionand, together with the description, serve to explain the principles ofthe invention. In the drawings:

FIG. 1 is a schematic representation of sound transmission through afluid-filled plane, parallel resonator cavity.

FIG. 2A is a graph showing the particle trapping positions, separated byλ_(F)/2, where <F>=0 located at the pressure nodes, while FIG. 2B is agraph of the direction of the force where <F>≠0 and <F> has a negativeslope, both for a plane parallel resonator.

FIG. 3A shows the location of the trapping positions for a positive(+ve) acoustic contrast factor (heavy, hard particles) and those for anegative (−ve) acoustic contrast factor (light, soft, particles), whileFIG. 3B is a graph of the acoustic contrast factor as a function of thedensity and compressibility ratio.

FIG. 4A is a schematic representation of an embodiment of aone-dimensional, parallel plate resonator apparatus, while FIG. 4B showsan arrangement of acoustic transducers for an embodiment of atwo-dimensional parallel-plate resonator apparatus.

FIGS. 5A-5C are representative particle patterns for one-dimensional,two-dimensional and three-dimensional application of orthogonal acousticwaves to a container of particles suspended in a host fluid,respectively.

FIG. 6 is a schematic representation of transducers disposed in anon-orthogonal configuration.

FIG. 7 is a schematic representation of an embodiment of a cylindricalacoustic resonator apparatus, illustrating the concentration ofparticles in periodic cylindrical patterns.

FIG. 8A is a graph showing an example of the acoustic radiation forcefor a cylindrical piezoelectric cavity, while FIG. 8B is a graph showingthe concentration profile for particles not having a uniform sizedistribution in a liquid suspension, wherein particles having largerdiameters will move to the center with smaller particles progressivelyremoved from the center.

FIG. 9 is a graph illustrating that acoustic forces may be generatedusing two-frequency mixing with the generation of beat frequencies inplace of a single applied resonant acoustic frequency.

FIG. 10A is a schematic representation of an elastic periodic structurehaving embedded expandable microspheres, while FIG. 10B is a graphillustrating the resonant frequency of such expandable microspheres as afunction of sphere radius.

DETAILED DESCRIPTION OF THE INVENTION

Briefly, embodiments of the present invention include apparatuses andmethods for using acoustical standing waves to create layers, or morecomplex patterns, in chosen materials, wherein selected suspendedparticles are disposed in a fluid form of the chosen material which maybe caused to harden. Transducers disposed on the sides of a container ofa chosen static quantity or batch of the suspension are adapted togenerate standing waves in the material. The suspended particles aredirected to the nodes or antinodes of the standing waves in response toacoustic forces generated therein. After the particles are permitted togather for a selected period of time, the fluid may be caused to harden,thereby fixing the pattern of suspended particles. The material may thenbe dissolved, leaving layers of suspended particles.

Embodiments of the invention further include the generation of suchmaterials (periodic structures on surfaces and in one-, two-, andthree-dimensions) with periodicities ranging from millimeter tosub-micrometer in length using a variety of host materials and particlecompositions, sizes, and shapes, such that the generated metamaterialsmay be used for both acoustical and optical applications. Out-of-planeresonators suitable for generating such three-dimensional bulkmetamaterials, and having large areas will be described.

Acoustic metamaterials may be manually created using large,millimeter-size objects; that is, for audio applications, the wavelengthof sound in air is large and larger structures are needed. For theultrasonic frequency range, wavelengths range between the micrometer andmillimeter scales. Ultrasonic frequencies are used in medicalapplications and for nondestructive testing, as examples. Sonic crystalsmay be used to create superlenses, which will allow imaging withsub-wavelength resolution that are not otherwise possible with otherlens materials. However, such small periodic structures are not readilygenerated by hand.

As stated hereinabove, photonic crystals may be fabricated in a planarfashion using photolithography, electron-beam lithography and otheretching techniques similar to those used for fabricating integratedcircuits, and quasi-three-dimensional metamaterials are achievable usinglayer-by-layer processing. Among the challenges in the fabrication ofthese structures is obtaining sufficient precision to prevent scatteringlosses from blurring the crystal properties; forming deep channels withsufficiently vertical walls; limitations in the choice of slab materialsthat can be anisotropically etched to form channels; physicallimitations of such slab materials that, in turn, can impose limitationson modulation schemes that might be realized; limited tunability ofparameters during and after the fabrication process; and, moregenerally, material cost, device yields, fabrication cost, and designflexibility. Other difficulties would be apparent to one skilled in theart upon reading the present disclosure.

Reference will now be made in detail to the present embodiments of theinvention, examples of which are illustrated in the accompanyingdrawings. In the FIGURES, similar structure will be identified usingidentical reference characters. Turning now to FIG. 1, soundtransmission through fluid-filled resonator cavity, 10, is illustrated.Flat transducers (piezoelectric crystals, as examples), 12 a, and 12 b,are attached to opposing sides, 14 a, and 14 b, of resonator cavity 10,which may be a fluid container having parallel walls, such as a cuvette.Transducer 12 a is excited by sine wave transmitter voltage signal, 16a, effective for generating sound waves in the fluid, and the amplitude,16 b, of the signal generated in opposing receiving transducer 12 b isobserved as an electrical signal converted by receiving transducer 12 b.When an integral number of half wavelengths (λ/2) of the sound wave inthe fluid exactly span the spacing, d, of parallel walls 14 a, 14 b ofcuvette 10, one may observe standing waves in the fluid between the twoopposite walls of the cuvette, and the sound transmission as a functionof frequency, reaches a maximum (resonance peak, shown as output 16 b).A series of such resonance peaks may be observed if the excitationfrequency is varied over a frequency range that satisfies the conditionfor the standing wave.

The sound speed of the wall material is generally higher than that forthe fluid inside the resonator cavity. If the frequency is varied over awide range, one observes a series of resonances where the soundtransmission peaks. At some frequencies, standing waves are generated inthe vessel wall; therefore, the observed resonance pattern is acombination of the resonance spectrum of the wall and that of the fluid.At frequencies where there are resonance peaks, a series of nodes andantinodes are established inside the resonator cavity. The spacing ofthe nodes and antinodes depends on the frequency of the excitationsignal.

The acoustic radiation force is interpreted as the time-averaged forceacting on an object in a sound field. This force is caused by a changein the energy density of an incident acoustic field. Thus, an object inthe wave path that absorbs or reflects sound energy is subjected to theacoustic radiation force. Small compressible spheres suspended in astanding acoustic wave field (for example, the standing wave set up in afluid inside a resonator cavity) experience a radiation force which hasthree separate components:

-   -   Primary acoustic force, F_(ac), which moves the spheres into the        node or anti-node planes of the acoustic displacement velocity;    -   Hydrodynamic Drag, F_(d), which affects the particles as they        move through the liquid under the influence of the acoustic        forces; and    -   Secondary acoustic force, F_(s), (Bjerknes Force) caused by the        scattered sonic field of a sphere, which causes nearby particles        to coagulate.

The primary acoustic forces in acoustic standing wave field can beexpressed as follows:

${F_{a\; c} = {\left\lceil \frac{P_{0}^{2}V_{p}\beta_{m}}{2\lambda_{m}} \right\rceil{\varphi\left( {B,\rho} \right)}{\sin\left( \frac{4\pi\; z}{\lambda_{m}} \right)}}},{where}$${{\varphi\left( {\beta,\rho} \right)} = \left( {\frac{{5\rho_{p}} - {2\rho_{m}}}{{2\rho_{p}} + \rho_{m}} - \frac{\beta_{p}}{\beta_{m}}} \right)},$V_(p)=particle volume; β=compressibility; ρ=density; λ=wavelength ofsound; P₀=Peak acoustic pressure; z=distance from pressure node; and m,p=medium, particle (subscripts).

If a particle having a size much smaller than the wavelength of sound inthe liquid is placed inside a resonator cavity where standing waves havebeen excited, it experiences a radiation force F that pushes theparticle to either the pressure node or anti-node depending on theacoustic contrast factor, φ, where the particle is trapped. The trappingpositions, 18 a, and 18 b, separated by λ/2 (FIG. 2A), are found where<F>=0 and where <F> has a negative slope for <F>≠0 as shown in FIG. 2B,hereof, for a plane parallel resonator. FIG. 2A further shows therelationship between the trapping locations and the pressure nodes andacoustic-wave velocity antinodes, respectively, for particles havingpositive φ.

If φ (the acoustic contrast factor) is positive (+ve), the particlesmove to the velocity antinodes, while if φ is negative (−ve), theparticles collect at the velocity nodes, as shown in FIGS. 3A and 3B.

As the particles move through the liquid under the influence of theacoustic forces mentioned hereinabove, they experience hydrodynamic dragwhich is given by the drag force

${F_{d} = {{- 4}{\pi\left\lbrack \frac{1 + {2{\hat{\mu}/3}}}{1 + \hat{\mu}} \right\rbrack}\mu\;{Rc}}},$where μ is the viscosity of the fluid, {circumflex over (μ)} is theratio of viscosity of the drop to the continuous phase and c is thespeed of the drop. When the particles move closer to the pressureantinodes and within a few diameters of another particle, a secondaryradiation attractive force between two spheres in an acoustic fielddominates. These inter-particle forces drive the particles together.

${F_{s} = {{- {\frac{k^{2}E_{a\; c}}{2\pi}\left\lbrack {1 - \frac{\beta_{p}}{\beta_{f}}} \right\rbrack}^{2}}\frac{V_{1}V_{2}}{d^{2}}}},$where, V₁ and V₂ are the volumes of the interacting droplets, and d isthe separation distance between the centers of the particles.

If there is an ensemble of particles of a given acoustic contrastfactor, these particles form a series of parallel planes, where theytightly bunch up due to the secondary force (the Bjerknes force). In thecase of droplets, coagulation takes place forming larger droplets.

A schematic representation of an embodiment of a one-dimensional,parallel plate resonator apparatus, 20, is shown in FIG. 4A. Digitalwaveform generator, 22, may generate a fixed-frequency sine wave, 24;other waveforms, such as a triangular waveform, a square wave, asexamples, may be effectively used. Sine wave signal 24 is directed intoamplifier, 25, although amplification may not be required, and output,26, is applied to transmitter transducer 12 a attached to flat plate 14a of glass cuvette 10 having square or rectangular geometry, andcross-sectional dimensions 2 cm×2 cm. The transmitter used was abroadband 5 MHz, center-frequency transducer having 2 cm diameter.Receiving transducer 12 b attached to opposing wall 14 b was identicalto transmitting transducer 12 a. The precise transducer employed dependson the periodicity of the standing wave pattern required; higherfrequencies being used for smaller spacings (periodicities). Thetransducers may be piezoelectric crystal plates or discs. Output signal,27, from receiving transducer 12 b was directed into amplifier, 28, andobserved on oscilloscope, 30. The excitation frequency 24 is varieduntil a maximum transmission signal was achieved. There are many suchpeak transmission frequencies (resonances), and one may chose aparticular frequency to obtain a desired standing wave pattern spacing.A frequency spectrum may be obtained by sweeping the waveform generator,observing the transmission spectrum and recording the resonance peakfrequencies. The strongest transmission signal is obtained in theneighborhood of a maximum in the wall resonance; the transducer centerfrequency may be chosen to match the peak of the wall resonance.However, other resonance peak frequencies may be chosen. Matching thefrequencies is useful for reducing heating of the fluid (for example, anepoxy). The excitation voltage level may then be adjusted to efficientlydrive the migration of the particles without significantly heating thefluid. Typically, the excitation may be increased by an order ofmagnitude to ≥10 V.

To produce sonic crystals, phononic crystals or acoustic metamaterials(where the particles are arranged in a periodic array of smallresonators) that are permanent (that is, where a 3-dimensional periodicpattern is maintained after the sonic field (and the resultant acousticradiation force) is withdrawn, the pattern must be fixed in anappropriate matrix. Further, the suspension is kept in a staticcondition during the formation of the pattern in order to reduceblurring of the patterns. To achieve this result, periodic patterns maybe captured in an epoxy, with the sonic field impressed on the system asthe epoxy solidifies (cures), leaving a permanent pattern after thesonic field is withdrawn. A UV-curable epoxy or an appropriate sol-gelhost system that solidifies with time may be used for more rapid curing.

One may also apply the same excitation signal to receiving transducer 12b through amplifier, 32, and switch, 34, to obtain excitation fromopposite sides of the cuvette instead of relying on the reflected soundto create the standing wave pattern. Depending on the impedances of thefluid and the walls of the cuvette, one may invert the excitation signalthat is applied to the receiving transducer. One can also use opposingtransducers, where both the phase and the frequency of the twotransducers can be varied to create additional patterns. Use of aparallel plate cuvette for containing the fluid-particle mixture wasprovided as an example; the cuvette may be replaced by a resonatorcavity having piezoelectric plates as sides.

The wavelengths of THz electromagnetic waves in air or any medium aresimilar to the wavelengths of ultrasonic waves in the MHz range for anyfluids or epoxies, as examples. Therefore, the same technique can beused for both optical metamaterials and acoustic metamaterials. Opticalmetamaterials affect electromagnetic wave propagation, whereas acousticmetamaterials affect elastic wave propagation. For opticalmetamaterials, negative refractive indices are observed, whereas theanalogous parameters for acoustic metamaterials are negative bulkmodulus and negative density. Embodiments of the present invention canthus create phononic or photonic crystals, which are periodic structureshaving periodicities on the order of wavelength, and wave diffractionand interference become relevant. The wavelengths referred to are thewavelengths of ultrasound or light used for the device application, andnot the wavelengths used in the creation of the pattern.

If a transparent cuvette is used, particle movement toward the variousnodes (or antinodes depending on the acoustic contrast factor of theparticles) may be observed. If the viscosity of the fluid issufficiently low, a pattern consisting of a series of parallel planes(reference character 36 in FIG. 4A) parallel to the parallel walls ofcuvette 10 is generally formed in between 10 s and 5 min. Forself-reacting epoxies (resin plus hardener), once the pattern isgenerated, the excitation signal is slowly lowered to zero while theepoxy is allowed to cure. If UV-curable epoxy is used, the pattern issolidified by directing UV light into the cuvette, after which theexcitation signal is turned off. Typically, the pattern-containing epoxyblock shrinks a small amount on all sides, making it straightforward toremove the solidified block from the cuvette.

Although commercially available epoxies have been employed to fix orsolidify the patterns, the patterns may also be solidified in otherpolymerizable monomers or short chain polymers, and by using sol-gelprocessing. Soft rubber as a host fluid has also been used to create apressure-tunable periodic structure (EXAMPLE 2, hereinbelow). Therefore,the embodiments of the present invention are not limited to epoxies, andappropriate host fluids that can be solidified by chemical reaction,applied heat or light, or any other external stimulation may be used.The appropriateness of the fluid relates in part to its acousticabsorption; that is, the absorption is such that the patterns can becreated having a desired spacing. For example, to create a patternhaving sub-micron periodicity, host fluids transparent to sound up to 20MHz are advantageous.

If the particle loading is large, cavity resonances tend to slightlyshift as the pattern is formed. This, in turn, lowers the radiationforce and the pattern formation rate is slightly reduced. A phase-lockedloop feedback controller (Not shown in FIG. 4A) may be included suchthat the phase of the received output signal is compared with the phaseof the excitation signal to the transmitter and the applied frequencyvaried to maintain this phase difference (at zero or 90 degrees, forexample) at a constant value. Such an electronic phase-locked systemprovides automatic control and may be used to correct for other systemchanges such as those caused by temperature variation or concentrationvariation as the pattern is formed. Clearly, there are many ways toimplement such system controls.

FIG. 4B illustrates a two-dimensional apparatus for the transmitting andreceiving transducers, 12 a and 38 a, and 12 b and 38 b, respectively.The pattern 36 of vertical parallel planes of particles in suspension asshown in FIG. 4A, are considered to fall in the one-dimensional category(FIG. 5A) because two opposing parallel plate transducers were used witha cuvette having a square cross-section. When orthogonal sound fieldsare applied such that two intersecting sound field patterns aregenerated, two-dimensional patterns may be produced (FIGS. 4B and 5B).The periodicity of the patterns in the orthogonal directions may bedifferent, thereby producing two standing wave patterns (frequencies),unless the same periodicity is required in both orthogonal directions.Moreover, the container may have other than rectangular cross-section.To produce a three-dimensional pattern, such as that shown in FIG. 5C,sound fields are generated in three orthogonal directions. As anexample, a cube-shaped cuvette having an open top and a cap fitting theopening having an attached transducer might be employed. Once theparticle-fluid mixture is introduced into the cuvette, the cap would beattached, forming thereby a cube having transducers attached to thethree orthogonal sides. In this situation, normally curing epoxy wouldbe used since it would be more difficult to introduce light into thesystem, as opposed to the visual access to the particle patternavailable for a one-dimensional system. For low concentrations ofparticles, the particles tend to collect at the acoustic waveintersections.

FIG. 6 is a schematic representation of transducers 12 a-12 c disposedin a non-orthogonal configuration.

Patterns may be generated using amplitude-modulated signals to generatestanding waves. In this situation, a high-frequency sound wave is usedas the carrier frequency that generates a pattern in the resonatorcavity. A lower frequency is used to modulate this carrier frequencysuch that a coarser standing wave pattern is also impressed on the fluidof interest. As an example, the carrier might produce 50 planes ofconcentrated particles, whereas the modulating frequency generates 5planes. One observes a pattern that comprises several planes locatedaround the 5 planes with the central planes having disappeared.

If two kinds of particles having positive (+ve) and negative (−ve)acoustic contrast factors (FIGS. 3A and 3B), a periodic patternalternating in the type of particle will result, wherein one typeparticle concentrates at the nodes, and the other particles concentrateat the antinodes. Further, if one mixes particles of the same kind buthaving different sizes, then the generated pattern will have the largerparticles in the center and the smaller particles on the outside, usefulfor applications such as the fabrication of light guides. A combinationof these embodiments may provide a large number of complex patterns thatare not possible to generate using traditional lithography methods.Additionally, lithographic techniques are generally applied to a smallclass of materials such as silicon, as an example, that are used inelectronic integrated circuits, and cannot be used for arbitraryparticles. By contrast, the acoustic radiation force is applicable toany type of particle, and patterns of particles may be created usingsuperconducting, dielectric, magnetic, piezoelectric, semiconducting,and metallic particles, and hollow microspheres, as examples, in avariety of host materials. This is not possible with another techniques,including the self-assembly techniques.

Embodiments of the present invention may be utilized for generatingperiodic structures which conform to the standing wave pattern of anyresonator system. For example, particles may be concentrated in periodiccylindrical patterns when a cylindrical resonator is employed, as shownin FIG. 7. Commercially available, 1.5 cm diameter, hollow cylindricalpiezoelectric element, 40, is filled with a suspension of particles in aliquid, and electrically excited at the thickness resonance mode of thecylinder wall, 42, by electrodes, 44, outside of the wall, and 46,inside the wall, such that sound waves are generated (˜1.5 MHz) anddevelop a standing wave pattern at the appropriate frequency. The numberof concentric cylinders formed depends on the frequency. An impedanceanalyzer was first used to determine the resonance spectrum of thisfluid-filled hollow cylinder, and the frequencies of interest wererecorded. The cylinder was then closed at the bottom end by adhesivetape, and the particle-epoxy mixture was introduced. A sine wave wasapplied by waveform generator 22 to the outer and inner electrodes onthe piezoelectric-cylinder and the excitation signal was increased.

Acoustic radiation forces move the particles to pressure nodes, 48,inside the cylinder. The particles were observed to concentrate asconcentric cylinders in a 3-dimensional pattern, in a similar manner topatterns for orthogonal geometry. The acoustic radiation forces for thecylindrical geometry are shown in FIG. 8A. Clearly, a large number ofstructures may be generated in accordance with embodiments of thepresent invention by choosing the appropriate resonator structure.

When particles are concentrated at the standing wave pressure nodes orantinodes, depending on the acoustic contrast factor of theparticle-host system, different sized particles experience differentlevels of force. If the particles in a liquid suspension do not have auniform size distribution, a concentration profile shown FIG. 8Bresults, wherein particles having the largest diameter will move to thecenter with smaller particles progressively removed from the center.

FIG. 9 is a graph illustrating that acoustic forces may be generatedusing two-frequency mixing with the generation of beat frequenciesinstead of using standing waves at a single applied acoustic frequency.

Having generally described embodiments of the present invention, thefollowing examples provide additional details.

Example 1

Particles having sizes varying from 5 nm diamond particles to 100 μmcarbon particles have been employed. The particles may have any shape,including spherical (10 μm polystyrene spheres were used). Particleswere suspended in 5-minute epoxy (for example, Devcon S-208), orUV-curable epoxy, and placed in cuvette 10 (FIG. 4A). The suspension wasstirred using a syringe to generate a homogenous mixture while the epoxywas unhardened. During this stirring and mixing, the ultrasonic signalwas not applied to the cuvette. After mixing, and after the frequencycorresponding to a resonance peak was determined, as describedhereinabove, the excitation signal was increased by an order ofmagnitude (typically, ≥10 V), and a pattern of parallel concentrationsof particles was generated.

Example 2

Gas-filled microspheres (Expancel®, vinylidene chloride, acrylonitrile,or methyl methacrylate, as examples) available in initial diameterranges between 6 μm and 40 μm, expand by factor of 60 by heating (FIG.10A). Microspheres are filled with a chosen gas (isobutane orisopentane, as examples). Elastic (soft rubber, as an example) periodicstructures generated in accordance with the teachings of the presentinvention behave as tunable micro-resonator system (acousticmetamaterial). FIG. 10B shows a graph of resonance frequency as afunction of the microsphere radius which may be altered by heating the3-dimensional structure.

Local microresonators may also be generated is the mass-spring systemwhere one can use a heavy particle coated with softer polymer material.The periodicity and size of the micro-resonators are less than ⅙^(th)the wavelength that will be used for its use. Since the wavelength ismuch larger than the periodicity or the size of the resonators, themedium behaves as an effective medium with negative properties.

Example 3

If the particles are in the form of cylinders, then acoustic radiationforces apply a torque to these cylinders, which align the cylindersparallel to each other. This effect was demonstrated using a mixture of80 μm carbon fibers in epoxy and then solidified. A slice of thesolidified block was observed under a scanning electron microscope (SEM)showed the parallel alignment of the carbon fibers. The method isapplicable to nanowires and nanotubes. Additionally, such structures, ifgenerated in a gel (for example, agar) or a bio-growth medium, may beuseful as a scaffolding for growing tissues and other biologicalmaterials.

In summary, embodiments of the present fabrication invention createperiodic structures in one-, two-, and three-dimensions, quickly andinexpensively using bench-top instrumentation since acoustic radiationforces do not discriminate among materials. The forces depend only onthe density and compressibility of a particle and not its materialproperties. As a result, many particle types may be used, including, butnot limited to metals; non-metals (insulators, non-conducting polymers,etc.); dielectrics; piezoelectric materials; paramagnetic materials;semiconductors; superconductors; nanotubes and nanowires; fibers; hollowor filled microspheres or tubes; and biological materials.

The foregoing description of the invention has been presented forpurposes of illustration and description and is not intended to beexhaustive or to limit the invention to the precise form disclosed, andobviously many modifications and variations are possible in light of theabove teaching. The embodiments were chosen and described in order tobest explain the principles of the invention and its practicalapplication to thereby enable others skilled in the art to best utilizethe invention in various embodiments and with various modifications asare suited to the particular use contemplated. It is intended that thescope of the invention be defined by the claims appended hereto.

What is claimed is:
 1. An apparatus for fabricating materials, theapparatus comprising: an acoustic resonator comprising a cavity definedby two sets of opposing, parallel spaced-apart resonator walls, each ofsaid walls having an outer surface and an acoustically reflecting innersurface configured to contain a static quantity of particles suspendedin a solidifiable fluid in said cavity; an acoustic transducer arrangedagainst the outer surface of at least one of the opposed walls of eachof the two sets of walls; a waveform generator configured to generate achosen waveform applied to each of the transducers to produce a chosenwavelength of intersecting acoustic standing waves in the bothsolidifiable fluid contained in said cavity and within each of the wallsof the two sets of walls for a sufficient time that the suspendedparticles migrate to pressure nodes or pressure antinodes of theintersecting standing waves to form a two-dimensional pattern of thesuspended particles in the solidifiable fluid; and means for solidifyingthe solidifiable fluid to form a solidified fluid fixing the formedtwo-dimensional pattern of particles therein.
 2. The apparatus of claim1, wherein the chosen wavelength, as λ, of the standing waves isselected such that a chosen number of the pressure nodes and a selectednumber of the pressure antinodes are generated in said acousticresonator.
 3. The apparatus of claim 2, wherein the pressure nodes arespaced apart by λ/2, and wherein the pressure antinodes are spaced apartby λ/2.
 4. The apparatus of claim 1, wherein the acoustic resonatorcavity is further defined by a third set of the opposing, parallelspaced-apart walls, whereby an acoustic transducer is arranged againstthe outer surface of one of the opposing walls of the third set ofwalls, wherein the waveform generator is further configured to generatethe chosen waveform applied also to the transducer of the third set ofwalls, and wherein the formed and fixed pattern is a three-dimensionalpattern of the particles.
 5. The apparatus of claim 4, wherein theacoustic resonator comprises a cube-shaped cuvette.
 6. The apparatus ofclaim 1, wherein the acoustic transducers are arranged against the outersurface of each of the opposed walls of each of the two sets of walls.7. The apparatus of claim 1, further configured to generate theintersecting standing waves orthogonal to one another.
 8. The apparatusof claim 1, wherein the particles are elongated, and wherein theelongated particles are oriented by the standing waves.
 9. The apparatusof claim 1, wherein the particles comprise hollow microspheres.
 10. Theapparatus of claim 9, wherein the hollow microspheres are expandablegas-filled microspheres, and wherein the solidified fluid is elastic.11. The apparatus of claim 1, wherein the particles comprise particlesof more than one composition.
 12. The apparatus of claim 1, wherein theparticles comprise particles having positive acoustic contrast factorsand particles having negative acoustic contrast factors.
 13. Theapparatus of claim 1, wherein the particles comprise particles havingmore than one size.
 14. The apparatus of claim 1, wherein the standingwaves are generated using amplitude-modulated acoustic carrierfrequencies produced by each of the transducers.
 15. The apparatus ofclaim 1, wherein the materials fabricated by the apparatus comprisephononic metamaterials.
 16. The apparatus of claim 1, wherein thematerials fabricated by the apparatus comprise photonic metamaterials.17. The apparatus of claim 1, wherein the fluid comprises at least oneepoxy.
 18. The apparatus of claim 1, wherein the solidified fluid isconfigured to be dissolved, thereby leaving layers of the suspendedparticles.
 19. The apparatus of claim 1, wherein the acoustic resonatorcomprises a glass cuvette having a square or rectangular geometry.